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A008277","chain":null}}],"oeis":[],"bfiles":[],"oeis_texts":[{"oeis_id":"","target":"node","first_row":0,"oeis_offset":0,"reversed":false,"trim_zeros":"none","regular_triangle":false,"rows_shown":10,"polytool_commit":"c48629374597092cc41ef4d6273f37991516f984","triangle_example":"Triangle begins:\n  0:               1;\n  1:              36,                 64,                    16;\n  2:            1296,               8704,                  9856,                   3072,                     256;\n  3:           46656,             953344,               2788096,                2396160,                  773120,                    98304,                     4096;\n  4:         1679616,           98320384,             638734336,             1148485632,               802185216,                253231104,                 38076416,                  2621440,                    65536;\n  5:        60466176,         9939533824,          134657560576,           455440465920,            582235095040,             343579557888,             103827505152,              16829644800,               1458831360,                62914560,                 1048576;\n  6:      2176782336,       997823217664,        27348044578816,        164957911252992,         356826781515776,          351335966834688,          179722337124352,           51532183633920,            8614730268672,            847081635840,             47706013696,             1409286144,              16777216;\n  7:     78364164096,     99921635835904,      5456042594861056,      56962878123540480,      199534996767375360,       308653182211325952,       246158588487139328,       111201498054000640,        30156496788520960,        5075480629739520,         536954345095168,         35395630792704,         1398481616896,          30064771072,           268435456;\n  8:   2821109907456,   9997178890092544,   1078978079459639296,   19155944710342705152,   105776295616693927936,    247871676604169060352,    293873602402040414208,    196503981318513623040,     79510550217970679808,    20382450772051230720,     3405268524506021888,     375887235574136832,     27393824326156288,     1293987746938880,      37838661877760,      618475290624,      4294967296;\n  9: 101559956668416, 999898440043331584, 212439477885296705536, 6344795235184111779840, 54277941881406048174080, 188176797258189002244096, 321701918451037345153024, 306356191444790799237120, 176108358772914231705600, 64542082932745206497280, 15652339673104306405376, 2573460414698474176512, 290733778126009008128, 22639603848006598656, 1204867124007272448, 42771277198393344, 962914487894016, 12369505812480, 68719476736;\n","recurrence_sentence":"The row polynomials satisfy P(n,x) = (36+64*x+16*x^2)*P(n-1,x) + (64*x+32*x^2)*d/dx P(n-1,x) + 16*x^2*d^2/dx^2 P(n-1,x) for n >= 1, with P(0,x) = 1.","mathematica":"P[0, x_] := 1;\nP[n_, x_] := P[n, x] = Expand[(36 + 64*x + 16*x^2)*P[n - 1, x] + (64*x + 32*x^2)*D[P[n - 1, x], x] + 16*x^2*D[P[n - 1, x], {x, 2}]];\nTable[CoefficientList[P[n, x], x], {n, 0, 9}] // Flatten","pari":"P(N) = {my(v = vector(N + 1)); v[1] = 1; for(n = 1, N, my(i = n + 1); v[i] = (36 + 64*x + 16*x^2)*v[i - 1] + (64*x + 32*x^2)*deriv(v[i - 1], x) + 16*x^2*deriv(deriv(v[i - 1], x), x)); v};\nrow(n, p) = {my(c = Vecrev(p)); c};\nT(N) = {my(v = P(N)); concat(vector(#v, i, row(i - 1, v[i])))};\nT(9)","reading":{"first_row":0,"offset":0,"reversed":false,"trim_zeros":"none","regular_triangle":false}}],"derivation":{"root":"n-08f49539099949d5","steps":["basis A013611","basis A008277"],"edges":["e-a6b5412d61e1c4e3","e-c793b959ef8a7384"],"text":"A034870 \u2192 basis A013611 \u2192 basis A008277"},"headline":"A034870 \u2192 basis A013611 \u2192 basis A008277","chain":null}